QAOA: A Way to Estimate Graph Optimization

Sources and Further Reading: Special acknowledgement to Michał Stęchły's "Musty Thoughts" blog posts on QAOA and VQE for making the core of this workshop possible, as well as his phenomenal presentation on behalf of the Warsaw Quantum Computing Group E. Farhi and J. Goldstone, "A Quantum Approximate Optimization Algorithm" http://arxiv.org/abs/1411.4028 Pranav Gokhale, Variational Quantum Eigensolver Demo https://www.youtube.com/watch?v=E947xs9-Mso Pranav Gokhale, VQE Demo: He-H+ https://github.com/singular-value/VQE_Demo/blob/master/VQE_Demo.ipynb Michał Stęchły, Variational Quantum Eigensolver Explained https://www.mustythoughts.com/variational-quantum-eigensolver-explained Michał Stęchły, WQCG Episode XX: 13.07.2020: Michał Stęchły "Variational Quantum Algorithms - how do they work?" https://www.youtube.com/watch?v=0simooIxb8Y Slides from above: https://docs.google.com/presentation/d/1TLv6ZO7OGOLlj49kWp5h9uSy398M_AFFprah2Q22_DU/edit#slide=id.g8bcc7dbab5_0_0 Entropica QAOA documentation, Cost function features and VQE, https://docs.entropicalabs.io/qaoa/notebooks/4_costfunctionsandvqe Michał Stęchły, Quantum Approximate Optimization Algorithm explained https://www.mustythoughts.com/quantum-approximate-optimization-algorithm-explained Rigetti Grove, Quantum Approximate Optimization Algorithm (QAOA) https://grove-docs.readthedocs.io/en/latest/qaoa.html Wolfram Mathworld, NP-Hard Problem https://mathworld.wolfram.com/NP-HardProblem.html Wolfram Mathworld, NP-Problem https://mathworld.wolfram.com/NP-Problem.html F. Glover et al., "Quantum Bridge Analytics I: A Tutorial on Formulating and Using QUBO Models" http://link.springer.com/10.1007/s10288-019-00424-y Catherine C. McGeoch, Adiabatic Quantum Computation and Quantum Annealing: Theory and Practice https://www.morganclaypool.com/doi/pdfplus/10.2200/S00585ED1V01Y201407QMC008?casa_token=fIZebH04dPsAAAAA%3Az6ZBb4MFtYbJvCDU1doa5q6OsETGK_E8VizrPbnRy-gdhnN_BV-hEsk7lfO1YgDbt1nQFUA8& Wikipedia, Traveling salesman Problem https://en.wikipedia.org/wiki/Travelling_salesman_problem Wolfram MathWorld, Traveling Salesman Problem https://mathworld.wolfram.com/TravelingSalesmanProblem.html Wolfram MathWorld, Hamiltonian Cycle https://mathworld.wolfram.com/HamiltonianCycle.html Formal definition of Traveling Salesman Problem by Professor Marc Goetschalckx: https://www2.isye.gatech.edu/~mgoetsch/cali/VEHICLE/TSP/TSP003__.HTM J.D. Cresser, Chapter 14 Probability, Expectation Value, and Uncertainty https://physics.mq.edu.au/~jcresser/Phys301/Chapters/Chapter14.pdf Tim Lam, Expectation Values https://people.physics.anu.edu.au/~cms130/phys2013/operators/expectation.html www.mathwords.com, Expected Value Mean of a Random Variable https://www.mathwords.com/e/expected_value.htm Michael G. Moore, PHYS851 Quantum Mechanics I, Fall 2009 Homework Assignment 13: Solutions https://web.pa.msu.edu/people/mmoore/851HW13_09Solutions.pdf Jack Ceroni, Intro to QAOA https://pennylane.ai/qml/demos/tutorial_qaoa_intro.html Qiskit Textbook, Solving combinatorial optimization problems using QAOA: https://qiskit.org/textbook/ch-applications/qaoa.html Qiskit Textbook, Lab 2: Quantum Measurement https://qiskit.org/textbook/ch-labs/Lab02_QuantumMeasurement.html Qiskit Textbook, Single Qubit Gates https://qiskit.org/textbook/ch-states/single-qubit-gates.html Ryan LaRose, Expectation Values, https://www.ryanlarose.com/uploads/1/1/5/8/115879647/quic04s02s.pdf Yi-Zhuang You, Quantum Mechanics Lecture Notes, Part 1. Qubits and Entanglement https://everettyou.github.io/teaching/PHYS212A/QubitsAndEntanglement.pdf Dr. Jens Eisert, Chapter 2 Quantum States and Observables https://www.physik.fu-berlin.de/en/einrichtungen/ag/ag-eisert/teaching/QMChapter2.pdf Google Quantum AI, Quantum variational algorithm https://quantumai.google/cirq/tutorials/variational_algorithm